Weak Values and Consistent Histories in Quantum Theory

A relation is obtained between weak values of quantum observables and the consistency criterion for histories of quantum events. It is shown that ``strange'' weak values for projection operators (such as values less than zero) always correspond to inconsistent families of histories. It is argued that using the ABL rule to obtain probabilities for counterfactual measurements corresponding to those strange weak values gives inconsistent results. This problem is shown to be remedied by using the conditional weight, or pseudo-probability, obtained from the multiple-time application of Luders' Rule. It is argued that an assumption of reverse causality (a form of time symmetry) implies that weak values obtain, in a restricted sense, at the time of the weak measurement as well as at the time of post-selection. Finally, it is argued that weak values are more appropriately characterised as multiple-time amplitudes than expectation values, and as such can have little to say about counterfactual questions.Comment: Final version, to appear in Studies in History and Philosophy of Modern Physic

Triaxial Galaxies with Cusps

We have constructed fully self-consistent models of triaxial galaxies with central density cusps. The triaxial generalizations of Dehnen's spherical models are presented, which have densities that vary as 1/r^gamma near the center and 1/r^4 at large radii. We computed libraries of about 7000 orbits in each of two triaxial models with gamma=1 (weak cusp) and gamma=2 (strong cusp); these two models have density profiles similar to those of the core and power-law galaxies observed by HST. Both mass models have short-to-long axis ratios of 1:2 and are maximally triaxial. A large fraction of the orbits in both model potentials are stochastic, as evidenced by their non-zero Liapunov exponents. We show that most of the stochastic orbits in the strong- cusp potential diffuse relatively quickly through their allowed phase-space volumes, on time scales of 100 - 1000 dynamical times. Stochastic orbits in the weak-cusp potential diffuse more slowly, often retaining their box-like shapes for 1000 dynamical times or longer. Attempts to construct self- consistent solutions using just the regular orbits failed for both mass models. Quasi-equilibrium solutions that include the stochastic orbits exist for both models; however, real galaxies constructed in this way would evolve near the center due to the continued mixing of the stochastic orbits. We attempted to construct more nearly stationary models in which stochastic phase space was uniformly populated at low energies. These ``fully mixed'' solutions were found to exist only for the weak-cusp potential. No significant fraction of the mass could be placed on fully-mixed stochastic orbits in the strong-cusp model, demonstrating that strong triaxiality can be inconsistent with a high central density.Comment: 58 TEX pages, 14 PostScript figures, uses epsf.st

Unsupervised Object Discovery and Tracking in Video Collections

This paper addresses the problem of automatically localizing dominant objects as spatio-temporal tubes in a noisy collection of videos with minimal or even no supervision. We formulate the problem as a combination of two complementary processes: discovery and tracking. The first one establishes correspondences between prominent regions across videos, and the second one associates successive similar object regions within the same video. Interestingly, our algorithm also discovers the implicit topology of frames associated with instances of the same object class across different videos, a role normally left to supervisory information in the form of class labels in conventional image and video understanding methods. Indeed, as demonstrated by our experiments, our method can handle video collections featuring multiple object classes, and substantially outperforms the state of the art in colocalization, even though it tackles a broader problem with much less supervision

Lopsidedness of self-consistent galaxies by the external field effect of clusters

Adopting Schwarzschild's orbit-superposition technique, we construct a series of self-consistent galaxy models, embedded in the external field of galaxy clusters in the framework of Milgrom's MOdified Newtonian Dynamics. These models represent relatively massive ellipticals with a Hernquist radial profile at various distances from the cluster centre. Using $N$-body simulations, we perform a first analysis of these models and their evolution. We find that self-gravitating axisymmetric density models, even under a weak external field, lose their symmetry by instability and generally evolve to triaxial configurations. A kinematic analysis suggests that the instability originates from both box and non-classified orbits with low angular momentum. We also consider a self-consistent isolated system which is then placed in a strong external field and allowed to evolve freely. This model, just as the corresponding equilibrium model in the same external field, eventually settles to a triaxial equilibrium as well, but has a higher velocity radial anisotropy and is rounder. The presence of an external field in MOND universe generically predicts some lopsidedness of galaxy shapes.Comment: 24 pages, 20 figures. Accepted for publication in Ap

Integrated cosmological probes: Concordance quantified

Assessing the consistency of parameter constraints derived from different cosmological probes is an important way to test the validity of the underlying cosmological model. In an earlier work [Nicola et al., 2017], we computed constraints on cosmological parameters for $\Lambda$CDM from an integrated analysis of CMB temperature anisotropies and CMB lensing from Planck, galaxy clustering and weak lensing from SDSS, weak lensing from DES SV as well as Type Ia supernovae and Hubble parameter measurements. In this work, we extend this analysis and quantify the concordance between the derived constraints and those derived by the Planck Collaboration as well as WMAP9, SPT and ACT. As a measure for consistency, we use the Surprise statistic [Seehars et al., 2014], which is based on the relative entropy. In the framework of a flat $\Lambda$CDM cosmological model, we find all data sets to be consistent with one another at a level of less than 1$\sigma$. We highlight that the relative entropy is sensitive to inconsistencies in the models that are used in different parts of the analysis. In particular, inconsistent assumptions for the neutrino mass break its invariance on the parameter choice. When consistent model assumptions are used, the data sets considered in this work all agree with each other and $\Lambda$CDM, without evidence for tensions.Comment: 17 pages, 4 figures, 2 tables, updated following referee's comments, now includes discussion of the Riess et al., 2016 Hubble parameter measurement, matches version accepted by JCA

EPR before EPR: a 1930 Einstein-Bohr thought experiment revisited

In 1930 Einstein argued against consistency of the time-energy uncertainty relation by discussing a thought experiment involving a measurement of mass of the box which emitted a photon. Bohr seemingly triumphed over Einstein by arguing that the Einstein's own general theory of relativity saves the consistency of quantum mechanics. We revisit this thought experiment from a modern point of view at a level suitable for undergraduate readership and find that neither Einstein nor Bohr was right. Instead, this thought experiment should be thought of as an early example of a system demonstrating nonlocal "EPR" quantum correlations, five years before the famous Einstein-Podolsky-Rosen paper.Comment: 11 pages, revised, accepted for publication in Eur. J. Phy

Square compactness and the filter extension property

We show that the consistency strength of κ being 2κ-square compact is at least weak compact and strictly less than indescribable. This is the first known improvement to the upper bound of strong compactness obtained in 1973 by Hajnal and Juhasz

Statistical tests of sterile neutrinos using cosmology and short-baseline data

In this paper we revisit the question of the information which cosmology provides on the scenarios with sterile neutrinos invoked to describe the SBL anomalies using Bayesian statistical tests. We perform an analysis of the cosmological data in $\Lambda$CDM$+r+\nu_s$ cosmologies for different cosmological data combinations, and obtain the marginalized cosmological likelihood in terms of the two relevant parameters, the sterile neutrino mass $m_s$ and its contribution to the energy density of the early Universe $N_{\rm eff}$. We then present an analysis to quantify at which level a model with one sterile neutrino is (dis)favoured with respect to a model with only three active neutrinos, using results from both short-baseline experiments and cosmology. We study the dependence of the results on the cosmological data considered, in particular on the inclusion of the recent BICEP2 results and the SZ cluster data from the Planck mission. We find that only when the cluster data is included the model with one extra sterile neutrino can become more favoured that the model with only the three active ones provided the sterile neutrino contribution to radiation density is suppressed with respect to the fully thermalized scenario. We have also quantified the level of (in)compatibility between the sterile neutrino masses implied by the cosmological and SBL results.Comment: 23 pages, 4 figure